Using approximate gradients in developing an interactive interior primal-dual multiobjective linear programming algorithm

Article Abstract:

A new interactive multi-objective linear programming is shown based on one variant of Karmarkar's algorithm or the path-following primal-dual algorithm. Karmarkar's algorithm is adapted for the multi-objective case by deriving an approximate gradient to the implicitly-known utility function. Through interactions with the decision maker, locally-relevant preference data are determined and the approximate gradient regularly updated. The interior step direction is determined by projecting the approximate gradient and taking an interior step from the current iterate to the new one in this projection.

Usage, Algorithms

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Time scale decomposition in production planning for unreliable flexible manufacturing systems

Article Abstract:

A group of stochastic control models for planning the operations of flexible manufacturing cells prone to random failure is derived. Such systems are characterized by the coupling between two stochastic process which have varying time-scales. The continuous-time models, which monitor the demand for different components and the influence of wear on machine failure, facilitate preventive maintenance or replacement. The models are used to implement a time-scale decomposition approach to enable simultaneous production planning and maintenance management.

Research, Management, Maintenance and repair, Stochastic processes, Production planning, Maintenance, Flexible manufacturing systems

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Using central prices in the decomposition of linear programs

Article Abstract:

A decomposition technique for solving the master program of large structured linear programming problems which offers faster convergence is presented. The technique generates cuts close to the analytic center of the solution set localization resulting in iterations with decreasing set localizations. The effectivity of the technique lies in its use of balanced central prices against conventional optimal price combinations of subproblems.

Decomposition (Mathematics)

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